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AlgoPlus//graph / dijkstra
Read the theory

Dijkstra's Shortest Path

Settle the nearest unvisited node, relax its edges.

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In a nutshell
Dijkstra's algorithm finds the shortest path from one start node to every other when edges carry costs (weights). It always settles the nearest unsettled node next — locking in its final distance — then relaxes its neighbours, checking whether routing through it is cheaper. A priority queue keeps the closest candidate handy. It assumes no edge weight is negative.
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A wavefront expands from the source, always settling the closest unvisited node first.
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Read the full theory, intuition & complexity for Dijkstra's Shortest Path.
Code Simulator
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def dijkstra(graph, start):
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    pq = [(0, start)]
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    dist = {n: inf for n in graph}
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    dist[start] = 0
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    while pq:
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        d, u = heappop(pq)  # Settle node
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        for v, w in graph[u]:
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            if dist[u] + w < dist[v]:  # Relax
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                dist[v] = dist[u] + w
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                heappush(pq, (dist[v], v))
Why Python? · Readable first, fast second

Dynamically typed and interpreted — every comparison and swap is dispatched by the interpreter at run time, so tight loops run roughly 10–100× slower than compiled C/C++. Unbeatable for learning the idea with the least code; not what you reach for when the inner loop is the bottleneck.